Eugene Borisovich Dynkin (russian: link=no, Евгений Борисович Дынкин; 11 May 1924 – 14 November 2014) was a

Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

and American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He made contributions to the fields of

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

and

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

, especially

semisimple In mathematics, semi-simplicity is a widespread concept in disciplines such as linear algebra, abstract algebra, representation theory, category theory, and algebraic geometry. A semi-simple object is one that can be decomposed into a sum of ''sim ...

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...

s, and

Markov process A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...

es. The

Dynkin diagram In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line). Dynkin diagrams arise in the classification of semisimple Lie algebras ...

, the

Dynkin system A Dynkin system, named after Eugene Dynkin is a collection of subsets of another universal set \Omega satisfying a set of axioms weaker than those of -algebra. Dynkin systems are sometimes referred to as -systems (Dynkin himself used this term) o ...

, and Dynkin's lemma are named after him.

Biography

Dynkin was born into a

Jew Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""Th ...

ish family, living in

Leningrad Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...

until 1935, when his family was exiled to

Kazakhstan Kazakhstan, officially the Republic of Kazakhstan, is a transcontinental country located mainly in Central Asia and partly in Eastern Europe. It borders Russia to the north and west, China to the east, Kyrgyzstan to the southeast, Uzbeki ...

. Two years later, when Dynkin was 13, his father disappeared in the

Gulag The Gulag, an acronym for , , "chief administration of the camps". The original name given to the system of camps controlled by the GPU was the Main Administration of Corrective Labor Camps (, )., name=, group= was the government agency in ...

Moscow University

At the age of 16, in 1940, Dynkin was admitted to

Moscow University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

. He avoided military service in

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

because of his poor eyesight, and received his MS in 1945 and his PhD in 1948. He became an assistant professor at Moscow, but was not awarded a "chair" until 1954 because of his political undesirability. His academic progress was made difficult due to his father's fate, as well as Dynkin's Jewish origin; the special efforts of

Andrey Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...

, his PhD supervisor, made it possible for Dynkin to progress through graduate school into a teaching position.

USSR Academy of Sciences

In 1968, Dynkin was forced to transfer from the Moscow University to the

Central Economic Mathematical Institute The Central Economic Mathematical Institute (russian: Центральный экономико-математический институт (ЦЭМИ)) of the Russian Academy of Sciences is an economic research institute located in Moscow. It fo ...

of the

USSR Academy of Sciences The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991, uniting the country's leading scientists, subordinated directly to the Council of Ministers of the Soviet Union (until 1946 ...

. He worked there on the theory of

economic growth Economic growth can be defined as the increase or improvement in the inflation-adjusted market value of the goods and services produced by an economy in a financial year. Statisticians conventionally measure such growth as the percent rate of ...

and

economic equilibrium In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the ( equilibrium) values of economic variables will not change. For example, in the st ...

Cornell

He remained at the Institute until 1976, when he emigrated to the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...

. In 1977, he became a professor at

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...

Death

Dynkin died at the

Cayuga Medical Center Cayuga Medical Center, officially referred to as Cayuga Medical Center at Ithaca and abbreviated as CMC, is a not-for-profit general hospital in Ithaca, New York, serving the residents of Broome, Cayuga, Chemung, Cortland, Schuyler, Seneca, ...

Ithaca Ithaca most commonly refers to: *Homer's Ithaca, an island featured in Homer's ''Odyssey'' *Ithaca (island), an island in Greece, possibly Homer's Ithaca *Ithaca, New York, a city, and home of Cornell University and Ithaca College Ithaca, Ithaka ...

New York New York most commonly refers to: * New York City, the most populous city in the United States, located in the state of New York * New York (state), a state in the northeastern United States New York may also refer to: Film and television * '' ...

, aged 90. Dynkin was an atheist.

Mathematical work

Dynkin is considered to be a rare example of a mathematician who made fundamental contributions to two very distinct areas of mathematics:

and

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

. The algebraic period of Dynkin's mathematical work was between 1944 and 1954, though even during this time a probabilistic theme was noticeable. Indeed, Dynkin's first publication was in 1945, jointly with N. A. Dmitriev, solved a problem on the

eigenvalue In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...

s of stochastic matrices. This problem was raised at Kolmogorov's seminar on

Markov chain A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...

s, while both Dynkin and Dmitriev were undergraduates.

Lie Theory

While Dynkin was a student at Moscow University, he attended

Israel Gelfand Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand ( yi, ישראל געלפֿאַנד, russian: Изра́иль Моисе́евич Гельфа́нд, uk, Ізраїль Мойсейович Гел� ...

's seminar on

s. In 1944, Gelfand asked him to prepare a survey on the structure and classification of semisimple Lie groups, based on the papers by

Hermann Weyl Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...

and

Bartel Leendert van der Waerden Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics. Biography Education and early career Van der Waerden learned advanced mathematics at the University of Amsterd ...

. Dynkin found the papers difficult to read, and in an attempt to better understand the results, he invented the notion of a "simple root" in a

root system In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties. The concept is fundamental in the theory of Lie groups and Lie algebras, especially the classification and representati ...

. He represented the pairwise angles between these simple roots in the form of a

. In this way he obtained a cleaner exposition of the classification of complex semisimple Lie algebras. Of Dynkin's 1947 paper "Structure of semisimple Lie algebras",

Bertram Kostant Bertram Kostant (May 24, 1928 – February 2, 2017) was an American mathematician who worked in representation theory, differential geometry, and mathematical physics. Early life and education Kostant grew up in New York City, where he gradua ...

wrote: Dynkin's 1952 influential paper "Semisimple subalgebras of semisimple Lie algebras", contained large tables and lists, and studied the subalgebras of the

exceptional Lie algebras Exception, exceptions or expectional may refer to: *Exception (computer science), an anomalous condition during computation * State of exception, a concept of extension of sovereign power * Exceptional objects, in mathematics ** Exceptional isomor ...

Probability theory

Dynkin is considered one of the founders of the modern theory of

es. The results obtained by Dynkin and other participants of his seminar at Moscow University were summarized in two books. The first of these, "Theory of Markov Processes", was published in 1959, and laid the foundations of the theory. Dynkin's one-hour talk at the 1962

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

Stockholm Stockholm () is the Capital city, capital and List of urban areas in Sweden by population, largest city of Sweden as well as the List of urban areas in the Nordic countries, largest urban area in Scandinavia. Approximately 980,000 people liv ...

, was delivered by Kolmogorov, since prior to his emigration, Dynkin was never permitted to travel to

the West West is a cardinal direction or compass point. West or The West may also refer to: Geography and locations Global context * The Western world * Western culture and Western civilization in general * The Western Bloc, countries allied with NATO ...

. This talk was titled "Markov processes and problems in analysis".

Prizes and awards

*Prize of the Moscow Mathematical Society, 1951 *Institute of Mathematical Statistics, Fellow, 1962 *American Academy of Arts and Sciences, Fellow, 1978 *National Academy of Sciences of the USA, Member, 1985 *American Mathematical Society,

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

for Total Mathematical Work, 1993 *Moscow Mathematical Society, Honorary Member, 1995 *Doctor Honoris Causa of the Pierre and Marie Curie University (Paris 6), 1997 *Doctor of Science (honoris causa) of the

University of Warwick The University of Warwick ( ; abbreviated as ''Warw.'' in post-nominal letters) is a public research university on the outskirts of Coventry between the West Midlands (county), West Midlands and Warwickshire, England. The university was founded i ...

, 2003. *Doctor Honoris Causa of the Independent Moscow University (Russia), 2003 *Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

, 2012

Publications

* * * * * * * *

Notes

External links

* *
Department listing at Cornell UniversityPersonal web pageCollection of interviews assembled by Dynkin
{{DEFAULTSORT:Dynkin, Eugene B. 1924 births 2014 deaths Jewish American atheists Fellows of the American Mathematical Society Members of the United States National Academy of Sciences 20th-century Russian mathematicians 20th-century American mathematicians 21st-century American mathematicians Soviet mathematicians Cornell University faculty Russian atheists Russian Jews Mathematicians from Saint Petersburg Algebraists Probability theorists Soviet emigrants to the United States Moscow State University alumni People from Saint Petersburg Measure theorists